According to Skaal legend, Solstheim history began with the dragon priest Vahlok sometime in the Merethic Era. He discovered that a dragon priest named Miraak was secretly plotting against his dragon overlords and confronted him. The two fought against each other for days in the northern part of Skyrim, and it was said to be so destructive that a piece of land was torn a part from the mainland of Skyrim. Thus, Solstheim was created.
Following the eruption of Red Mountain in 4E 5, thousands of Dunmer were forced to flee Morrowind. Many crossed over the border into Skyrim seeking refuge, and whilst they were accommodated, the Nords graciously offered them the island of Solstheim as their new home. The High King of Skyrim gave them this territory formally in 4E 16. 
The geography of the island bears similar traits to both Vvardenfell and Skyrim. The north is dominated by the arctic climate similar to that found in Winterhold Hold, while the south features the jagged landscape reminiscent of the Dunmer homeland.
The High King of Skyrim gave Solstheim to the Dunmer refugees in 4E 16. Since then, they have ruled over Solstheim along with the Skaal who were inhabitated on the island before them.
The Daedric Prince, Hircine, is known to have significant influence over the island and its people. Hircine is able to physically manifest for a hunt on Solstheim with his werewolf minions, at the ending of every era. The Skaal call this destructive event the Bloodmoon Prophecy, for as Hircine arrives, the moons turn as red as blood. This indicates that the Bloodmoon Prophecy will happen again in the end of the 4th era.
The Daedric Prince, Hermaeus Mora, is also known to have some influence on the island.